Boyle's Law

Plug the pressure sensor into the adapter cable
in Channel 1 of the CBL. Connect a 20-mL syringe to the 3-way
valve.

Connect the CBL System to the TI-8X calculator
with the link cable using the port located on the bottom edge of
each unit. Firmly press in the cable ends.

Open the side arm of the pressure sensor valve to
allow air to enter and exit. If your pressure sensor has a metal
valve, open its side valve by turning the knob one turn
counterclockwise. If your pressure sensor has a plastic valve,
open its side valve by aligning the blue handle with the arm that
leads to the pressure sensor (see Figure).

Move the piston of the syringe until the front
edge of the inside black ring is positioned at the 10.0 mL
mark.

Close the side arm of the pressure sensor valve.
If the valve is metal, firmly turn the knob clockwise to close it.
If the valve is plastic, align the blue handle with the side
arm.

2. Turn on the CBL unit and the TI-8X calculator.
Press PRGM and select CHEMBIO. Press ENTER, then press ENTER again to
go to the CHEM MAIN MENU.

3. Set up the calculator and CBL for a pressure
sensor and calibration (in atmospheres).

Select SET UP PROBES from the CHEM MAIN
MENU.

Enter "1" as the number of probes.

Select PRESSURE from the SELECT PROBE
menu.

Enter "1" as the channel number.

Select USE STORED from the CALIBRATION
menu.

Select ATM from the PRESSURE UNITS menu.

4. Set up the calculator and CBL for data
collection.

Select COLLECT DATA from the CHEM MAIN
MENU.

Select TRIGGER/PROMPT from the DATA COLLECTION
menu.

5. Collect the pressure versus volume data. It is
best for one person to take care of the gas syringe and for another
to operate the calculator.

Move the piston to position the front edge of the
inside black ring at the 5.0 mL line on the syringe. Hold the
piston firmly in this position until the pressure value displayed
on the CBL stabilizes.

When the pressure reading has stabilized, press
TRIGGER on the CBL. Type in the gas volume (in mL) on the
calculator. Press the ENTER key to store this pressure-volume data
pair.

7. STOP AND GRAPH from the DATA COLLECTION menu when
you have finished collecting data. Use RIGHT ARROW to examine the
data points along the displayed graph of pressure vs. volume. As you
move the cursor right or left, the volume (X) and pressure (Y) values
of each data point are displayed below the graph. Record the pressure
(round to the nearest 0.01 atm) and volume data pairs in your
data table.

8. Based on the graph of pressure vs. volume, decide
what kind of mathematical relationship you think exists between these
two variables, direct or inverse. To see if you made the right
choice:

Press ENTER, then select NO when asked if you
want to repeat. Select QUIT to quit the data collection
program.

Press STAT, RIGHT ARROW to display the CALC menu.
Use the down-arrow key to scroll to the bottom item of the menu
and select PwrReg.

Press [2nd],[L1][2nd],[L 2],ENTER. The
power-regression statistics for these two lists are displayed for
the equation in the form:

y = a*x^b (y =
a*xb)

where x is volume, y is pressure, a is a
proportionality constant, and b is the exponent of x (volume) in
this equation. Note: The relationship between pressure and volume
can be determined from the value and sign of the exponent,
b.

To display the power-regression curve on the
graph of pressure vs. volume, first press Y=. Press CLEAR to clear
the Y1= equation, then press VARS. Select Statistics and press
RIGHT ARROW, RIGHT ARROW to display the EQ menu. Select RegEQ to
copy the power regression equation to Y1=.

Press WINDOW and then set Xmin = 0 and Ymin = 0
(so both axes are scaled from 0).

Press GRAPH to plot pressure vs. volume with the
power-regression curve for your data. If you have correctly
determined the mathematical relationship, the power regression
line should very nearly fit the points on the graph (that is, pass
through or near the plotted points).

Questions

1. If the volume is doubled from 5.0 mL to 10.0 mL,
what does your data show happens to the pressure? Show the pressure
values in your answer.

2. If the volume is halved from 20.0 mL to 10.0 mL,
what does your data show happens to the pressure? Show the pressure
values in your answer.

3. If the volume is tripled from 5.0 mL to 15.0 mL,
what does your data show happened to the pressure? Show the pressure
values in your answer.

4. From your answers to the first three questions and
the shape of the curve in the plot of pressure versus volume, do you
think the relationship between the pressure and volume of a confined
gas is direct or inverse? Explain your answer.

5. Based on your data, what would you expect the
pressure to be if the volume of the syringe was increased to 40.0 mL.
Explain or show work to support your answer.

6. Based on your data, what would you expect the
pressure to be if the volume of the syringe was decreased to 2.5
mL.

7. What experimental factors are assumed to be
constant in this experiment?

8. One way to determine if a relationship is inverse
or direct is to find a proportionality constant, k, from the data. If
this relationship is direct, k = P/V. If it is inverse, k = PxV.
Based on your answer to Question 4, choose one of these formulas and
calculate k for the seven ordered pairs in your data table (divide or
multiply the P and V values). Show the answers in the third column of
the Data and Calculations table.

9. How constant were the values for k you obtained in
Question 8? Good data may show some minor variation, but the values
for k should be relatively constant.

11. To confirm that an inverse relationship exists
between pressure and volume, a graph of pressure vs. reciprocal of
volume (1/volume or
volume-1) may also
be plotted. To do this using your TI-83 calculator, it is necessary
to create a new data list, reciprocal of volume, based on your
original volume data.